1. Field of the Invention
This disclosure relates generally to the field of building numerical models suitable for computer simulation of diffusive processes in heterogeneous media, such as fluid flow in underground porous rock formations like oil and gas reservoirs and/or aquifers.
2. Description of Related Art
Computer simulation of fluid flow in porous media is widely used in the oil industry, hydrology, environmental studies, and remediation of contaminated groundwater. Simulation predictions often have a significant impact on the economic valuation of assets and government environmental policies. This invention is related to a key step in building accurate simulation models. In the preferred embodiments, reference is made to the application of the disclosure to hydrocarbon recovery, but the scope of the invention is not limited to the simulation of hydrocarbon recovery.
Very often, there is a need to compute a velocity vector field consistent with a set of fluxes given with respect to a structured or unstructured simulation grid. Since many fluid flow simulators use Finite Difference (FD) or Control Volume discretizations, they do not compute a fluid velocity vector field directly but rather generate a set of fluxes on cell faces. Therefore, there is the need to convert a set a fluxes into a velocity field.
Once an explicit velocity vector field is available, it may be used to compute streamlines and dispersion tensor coefficients. Streamlines can be used for visualization or streamline simulations.
Another example of using a velocity vector field is to compare fluxes computed on a fine grid to fluxes on several coarse grids for the purpose of evaluating the quality of different coarse (simulation scale) grids. Similarly, one could use such fine-coarse grid flux comparisons for evaluating and/or generating upscaled reservoir properties. Also, fluxes may be used to convert from an unstructured grid to a structured grid for visualization purposes. A comparison of fluxes computed on unstructured and structured grids can be used for testing and validating the computer code that uses the unstructured grid discretization. In particular, the effect of non-orthogonalities in the grid upon the accuracy of the computed fluxes may be tested. Since flux comparison is local, it could help pinpoint problem areas.
Comparing fluxes computed with respect to different grids is a non-trivial task. Although, strictly speaking, fluxes are scalars, they contain geometric information which has to be taken into account for any meaningful comparison. This geometric information includes the area and the orientation of the surface with respect to which the fluxes are computed. The problem of comparing fluxes on different grids is somewhat similar to comparing two vectors with components given with respect to two different coordinate systems. In order to obtain a meaningful comparison, one needs to know the components of the two vectors with respect to the same coordinate system. Similarly, one needs to transfer the two fluxes to a single grid in order to be able to perform a meaningful comparison. As a transfer mechanism, we suggest using a physically realistic velocity vector field, which is defined at every point and is computed using the unstructured grid fluxes, the grid-block geometry, and the underlying permeability field.